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Solutions to this puzzle came in from Shauneen from Our Lady's Grammar School , Newry; Claire and Amy of Madras College, St Andrew's; Nicola and Rosie of Maidstone Grammar School for Girls and Chris, Sarah, Jack, Laura, Jan and Michael from Necton Middle School, Norfolk . An equivalent (dual) solution to the one illustrated is obtained by swapping the numbers at the vertices with the numbers on the faces.
Each of these solids is made up with 3 squares and a triangle around each vertex. Each has a total of 18 square faces and 8 faces that are equilateral triangles. How many faces, edges and vertices does each solid have?
This problem is about investigating whether it is possible to start at one vertex of a platonic solid and visit every other vertex once only returning to the vertex you started at.
Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?